sign in sign up
<<
Home , Pattern, Prior Analytics, Sophistical Refutations

University of Windsor Scholarship at UWindsor

OSSA Conference Archive OSSA 2

May 15th, 9:00 AM - May 17th, 5:00 PM

Aristotle’s Treatment of Fallacious Reasoning in and

George Boger Canisius College

Follow this and additional works at: https://scholar.uwindsor.ca/ossaarchive

Part of the Philosophy Commons

Boger, George, "’s Treatment of Fallacious Reasoning in Sophistical Refutations and Prior Analytics" (1997). OSSA Conference Archive. 12. https://scholar.uwindsor.ca/ossaarchive/OSSA2/papersandcommentaries/12

This Paper is brought to you for free and open access by the Conferences and Conference Proceedings at Scholarship at UWindsor. It has been accepted for inclusion in OSSA Conference Archive by an authorized conference organizer of Scholarship at UWindsor. For more , please contact [email protected]. ARISTOTLE ON FALLACIOUS REASONING IN SOPHISTICAL REFUTATIONS AND PRIOR ANALYTICS

George Boger Department of Philosophy Canisius College ©1998, George Boger

Abstract: Aristotle studies syllogistic argumentation in Sophistical Refutations and Prior Analytics. In the latter he focuses on the formal and syntactic character of arguments and treats the sullogismoi and non- sullogismoi as argument patterns with valid or invalid instances. In the former Aristotle focuses on semantics and to study apparent sullogismoi as arguments. Interpreters usually take Sophistical Refutations as considerably less mature than Prior Analytics. Our interpretation holds that the two works are more of a piece than previously believed and, indeed, that Aristotle's treatment of fallacious reasoning presupposes the results of the formal theory.

***

1. Introduction.

Aristotle defines "sullogismos" () in , Sophistical Refutations, Rhetoric, and Prior Analytics in virtually the same way: "a sullogismos is a discourse [logos] in which, certain things having been supposed, something different from the things supposed necessarily results".1 Interpreters of Aristotle's customarily take a sullogismos to be a topic specific, object language argument or deduction and not to be a topic neutral argument form or pattern. Interpreters also customarily believe Sophistical Refutations and Topics to be considerably less mature than Prior Analytics, and, accordingly, they have not studied the one in relation to the other.

While Aristotle does treat a sullogismos in Sophistical Refutations as an object language phenomenon, it is evident that he specifically treats the sullogismoi and non-sullogismoi in Prior Analytics A4-7 as topic neutral argument forms or argument patterns whose instances are either valid or invalid arguments. In Prior Analytics Aristotle establishes all the argument patterns whose instances are valid arguments-that is, all the sullogismoi of the three figures-by means of metalogical deductions. And he just as surely establishes metalogically all the argument patterns whose instances are invalid arguments-that is, all the non-sullogismoi-by means of the method of contrasted instances. His logical investigations at Prior Analytics A4-7 are strictly formal and syntactic. In Sophistical Refutations he defines a sullogismos just as at Prior Analytics, and he defines a refutation (elenchos) as "a sullogismos whose conclusion is the contradiction of a given statement". But there he systematically treats actual arguments, in particular, those than appear to be valid but are really only apparent or phainomenoi sullogismoi and sophistical refutations or sophistikoi elenchoi. The emphasis, then, in Sophistical Refutations is on semantic and rhetorical matters having to do with argumentation.

Modern interpreters have referred to the of Sophistical Refutations as "informal " without regard to the formal results of Prior Analytics as both works bear on the practice of argumentation. We believe that Aristotle's logical investigations in Sophistical Refutations, which emphasizes semantics, are better understood in relation to his syntactic considerations in Prior Analytics, that Sophistical Refutations and Prior Analytics (indeed, that all the treatises of the ) are more of a piece that previously believed. We aim to show that Aristotle's treatment of the fallacies depending on and those not depending on language may presuppose the formal results of Prior Analytics A4-7. In this respect, we take Aristotle more determinately to distinguish semantics and logical syntax than have previous interpreters. Accordingly, we can better appreciate Aristotle's original contributions to formal logic and to the study of argumentation.

2. Misinterpreting Aristotle's project in Prior Analytics

Three principal interpretive trends characterize studies of Aristotle's logical investigations. The deductionist interpretation mathematically models Aristotle's logic as a natural deduction system. J. Corcoran, T. Smiley, and R. Smith consider a sullogismos to be a deduction-a fully interpreted argumentation having a cogent chain of reasoning in addition to premises and conclusion. The axiomaticist interpretation takes Prior Analytics to lay out an axiomatized deductive system of syllogistic theorems. J. Lukasiewicz, I. M. Bochenski, and G. Patzig take a sullogismos to be a single, relatively uninterpreted, logically true conditional proposition. Only the traditionalist interpretation continues to hold that Prior Analytics is a logic manual for studying categorical arguments or . Proponents such as J. N. Keynes, R. M. Eaton, and W. D. Ross usually treat a sullogismos as a fully interpreted, valid or invalid premise-conclusion argument.

Notwithstanding important differences, these interpretations hold quite similar views concerning Aristotle's methods for establishing knowledge of invalidity. However, none of these interpretations provides an account that fits the text of Prior Analytics. On the one hand, traditionalists usually apply six rules of the syllogism, namely, those pertaining to , quantity, and distribution.2 This certainly does not resemble any practice of Aristotle. Axiomaticist and deductionist interpreters, on the other hand, equally take Aristotle (1) to consider arguments or deductions and (2) to use the method of counterargument. On both counts they are mistaken. First, Aristotle does not especially treat arguments or deductions in Prior Analytics A4-7. Rather, with a view toward their corresponding argument patterns, he expressly treats patterns of two categorical sentences or premise-pair patterns. Second, there is no instance of Aristotle explicitly using the method of counterargument as is commonly maintained by interpreters such as J. Lukasiewicz (1958: 70) and J. Corcoran (1974: 105, 1989: 31; cf. 1993: xxxi). Rather, he principally uses the method of constrasted instances (W. D. Ross 1949) to invalidate premise-pair patterns and, consequently, their four corresponding argument patterns.

Our interpretive standpoint takes Aristotle in Prior Analytics as verifying the results of his constructing a natural deduction system. At A4-7 Aristotle exhaustively treats only and all possible combinations of three different terms in premise-pair patterns to demonstrate (1) which pair patterns are concludent and generate a sullogismos and (2) which pair patterns are inconcludent and do not generate a sullogismos (see G. Patzig 1968 and L. Rose 1968). Accordingly, we hold that a sullogismos as treated in Prior Analytics A4-7 is neither a valid or invalid premise- conclusion argument, nor a single, logically true conditional proposition, nor a deduction. Rather, as a relatively uninterpreted object, it is an elemental argument pattern in one of three figures, consisting in a premise-set of two categorical sentence patterns and a conclusion of a single categorical sentence pattern and having all valid argument instances. Aristotle recognized the epistemic efficacy of such elemental patterns and formulated them in corresponding sentences to express rules of deduction. Section three below addresses how Aristotle eliminates argument patterns unproductive of deduction rules and, thus, how he identifies invalid arguments and fallacious reasoning from formal considerations.

3.0 Some preliminary matters 3.1 Logic terminology. We use the following terminology, following J. Corcoran 1989 and 1993, to examine Aristotle's logic.3 An argument is a two part system consisting in a set of sentences in the role of premises and a single sentence in the role of conclusion; an argument is either valid or invalid. A sentence is either true or false. An argumentation is a three part system consisting in a chain of reasoning in addition to premises and conclusion and is either cogent, in which case it is a deduction, or fallacious, a non-deduction. A sentence, an argument, and an argumentation are object language phenomena. An argument pattern is a two part system consisting in a set of sentence patterns in the role of a premise-set and a single sentence pattern in the role of conclusion. A pattern is a metalinguistic object distinguishable from a form and is commonly represented schematically (see below note 11 on distinguishing "form" and "pattern"). An argument is said to fit or to be an instance of one or more argument patterns. A given argument pattern may have all valid instances, all invalid instances, or some valid and some invalid instances. An argument pattern is not properly valid or invalid, although logicians have used "valid" in this connection. Corcoran (1993: xxxiv-xxxv) has helped to clarify category differences here by using the following terminology: an argument pattern with all valid instances is panvalid, that with all invalid instances is paninvalid, and that having instances of both is neutrovalid. We add that an elemental panvalid argument pattern is one having a simple premise-set pattern whose epistemic consists in its "immediately" evident to someone that its conclusion follows necessarily. An elemental argument pattern may be formulated in a corresponding sentence to express a rule of deduction. In addition, we follow G. Patzig to distinguish in Aristotle's logic a concludent pattern of two protasesis or a premise-pair pattern from an inconcludent premise-pair pattern. A concludent pattern has a necessary result, that is, it results in a sullogismos, while an inconcludent pattern has no necessary result and cannot result in a sullogismos.

3.2 Aristotle's focus on logical syntax in Prior Analytics. Aristotle knew that deductions about geometric objects are topic specific and that they employ a topic neutral deduction system,4 even if that system is used implicitly by a participant. In Prior Analytics he turned his attention not to geometric or biological objects, nor even to geometric or biological discourses, but to the deduction apparatus used to make evident that a given categorical sentence necessarily follows from other given categorical sentences. Aristotle had observed a number of elemental argument patterns in various object language discourses, some of which he recognized always to result in something following necessarily, others of which he recognized never to result in something following necessarily. He subsequently extracted these patterns for systematic examination. In Prior Analytics Aristotle models his syllogistic logic and presents the results of his investigations.5 In this connection, then, Prior Analytics is a scientific study of the syllogistic deduction system, which, taken with and , comprises Aristotle's treatment of the syllogistic underlying logic.

The results of our study of Prior Analytics show that there a sullogismos is not a fully interpreted object according to an intended in a given topical sub-language, and that Aristotle distinguishes logical syntax from semantics. One way sufficient for determining whether or not a logician distinguishes logical syntax from semantics is to ascertain whether a logician works with a of substitution (in contrast to a notion of "interpretation"). In a substitution one changes the language, or the content words and phrases in a given language, while leaving their meanings and the fixed. In this light, observing Aristotle's pervasive use of schematic letters and his practice of substitution for establishing inconcludence, we recognize him more determinately to distinguish semantics and logical syntax and, indeed, to focus on the patterns of valid and invalid arguments at A4-7.

Aristotle's syllogistic syntax. The following practices in treating an underlying logic as a subject matter indicate Aristotle's attention on formal considerations apart from particular subject matters. (1) Aristotle systematically treats patterns of two protaseis or premise-pair patterns and their corresponding argument patterns and treats neither premises nor arguments themselves. Arguments are introduced to establish that certain premise-pair patterns are inconcludent. (2) Aristotle uses three sets of schematic letters to mark places for terms, one set for each figure (schema). He names terms by their schematic positions-first (or major), middle, last (or minor)-and he calls the first and last extremes (akra). Most significant, perhaps, is (3) Aristotle's treating categorical sentence patterns schematically with a strict syntax. His common schematic representations of the four kinds of categorical sentence are:

A belongs to every B A belongs to no B A belongs to some B A does not belong to some B.

Here 'A' and 'B' are schematic letters6 marking places for the predicate and subject terms respectively. Although Aristotle does not abbreviate each of the four logical constants with a letter as modern logicians, namely, with 'a', 'e', 'i', and 'o', he names them just as modern logicians do (A4, 26b30-33):

belongs to every (a) belongs to none (e)

belongs to some (i) does not belong to some (o).

Thus, using Aristotle's schematic letters and our abbreviations for the logical constants, we may represent the four categorical sentence patterns schematically as 'AaB', 'AeB', 'AiB', and 'AoB'. Finally, (4) throughout A4-6 Aristotle works with schematic letters for three terms in various premise-pair patterns according to three figures. In every case, whatever order he presents the 'sentences' in a premise-pair pattern, that is, whether he states first the major or the minor premise pattern, he always understands the predicate term (P) of the conclusion pattern (PxS) to be the first term in the premise-pair pattern and the subject term (S) of the conclusion pattern to be the last term ('P' and 'S'are schematic letters and 'x' holds a place for one of Aristotle's four logical constants). This syntax is strict. He always considers the conclusion of an argument to fit the sentence pattern PxS and not its converse.7 A familiar way of schematically representing the standard syntax of the three figures follows (the 'premises' are numbered and the 'conclusion is indicated by '?')

First figure Second figure Third figure

PxM, MxS | PxS MxP, MxS | PxS PxM, SxM | PxS

1. PxM 1. MxP 1. PxM

2. MxS 2. MxS 2. SxM

? PxS ? PxS ? PxS

Aristotle is well aware of a distinction between syntax and semantics, indeed, in a way familiar to A. Church, A. Tarski and other modern logicians.

3.3 Establishing the sullogismoi. At A5-6 Aristotle uses a natural deduction system-which consists in four kinds of categorical sentence, two pairs of contradictories and one pair of contraries, three conversion rules, four teleioi- sullogismoi, and two kinds of proof (direct and indirect)-to show that a given second or third figure argument pattern is, in fact, a sullogismos. In each case Aristotle demonstrates by means of a metalogical deduction that a given premise-pair pattern generates a sullogismos with a certain conclusion. The text concerning Camestres (27a9-14) makes this evident.8

If M belongs to every N but to no X, then neither will N belong to any X. For if M belongs to no X, neither does X belong to any M; but M belonged to every N; therefore, X will belong to no N (for the first figure has again been generated). And since the privative converts, neither will N belong to any X.

We can exactly express what Aristotle writes here in the familiar manner of a modern deduction.

1.MaN 2.MeX ?NeX

3.MeX 2 repetition 4.XeM 3 e-conversion 5.MaN 1 repetition 6.XeN 4, 5 Celarent 7.NeX 6 e-conversion

Every second and third figure sullogismos is determined in just this manner, whether by direct or indirect deduction. Thus, he establishes all the panvalid elemental argument patterns or sullogismoi in this way.9 Every argument with semantically precise terms fitting one of these patterns is valid.

3.4 Aristotle's notion of "following necessarily".10 Aristotle defines "that which is necessary" in 5.5 as "that having no other relationship possible" (1015a34). At Metaphysics 4.5 he writes much the same: "for it is not possible for what is necessary to be one way and another way, and so if something is of necessity, it cannot be so and not so" (1010b28-30). Respecting a demonstration he writes that "if there is a sullogismos it is [logically] impossible for there to be another relationship among them [i.e. three terms in two premises]" (1015b7-9). The statements defining "necessary" in Metaphysics 4.5 and 5.5 (see also 1011b13-14; cf 6) certainly help to inform our understanding of Aristotle's of a sullogismos in Prior Analytics A1 (24b18- 22): "a sullogismos is a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so" (24b18-20; emphasis added). In Prior Analytics he summarizes his findings concerning the sullogismoi: "it is evident both that a sullogismos is generated necessarily whenever the terms are related to one another as was stated, and that if there is a sullogismos, then it is necessary for the terms to be so related" (A5, 28a1-3; cf. A6, 29a11-14). For there to be a sullogismos it is necessary and sufficient that the terms be formally related as Aristotle states, albeit tersely, in a number of rules. Likewise, as we shall see below (section 4.4), for there not to be a sullogismos it is necessary and sufficient that terms be formally related in the other ways he systematically covers.

4.0 Establishing invalidity in Prior Analytics.

4.1. Modern methods for determining invalidity. Modern logicians most often use six methods to determine that a given arbitrary argument is invalid: (1) the method of fact; (2) the method of counterargument and its variant the method of counterinterpretation; (3) the method of deduction or the axiomatic method, sometimes called reduction; (4) the method of tables; and, in relation to traditional Aristotelian logic, there are (5) the traditionalist method of applying rules of the syllogism and (6) the methods of Venn and Euler diagrams. Aristotle no doubt was familiar with the method of fact; otherwise, he applied none of these methods except, perhaps in some instances, a variation of the axiomatic method. We briefly review only the methods of fact and counterargument to help establish that Aristotle's method of contrasted instances is a different method.

The method of fact. A given argument is determined to be invalid when the premises are known to be true sentences and the conclusion is known to be a false sentence. Knowledge that the premises are true and that the conclusion is false is sufficient to determine that a given argument is invalid. The ontic underlying the application of this method holds that no argument is valid whose premises are true and whose conclusion is false. The following example of an obviously invalid argument illustrates this method (premises numbered, the conclusion indicated by the '?'):

1.Every even number divides itself.(T) 2.Every odd number divides itself. (T) ? Every even number divides every odd number.(F)

The method of counterargument. A given argument is determined to be invalid when a counterargument is exhibited for the given argument. A counterargument for a given argument is an argument having all true premises and a false conclusion and is in the same form as the given argument. Knowing that a counterargument exists for a given argument is sufficient for establishing knowledge that the given argument is invalid. The method of fact underlies applying the method of counterargument. The method of counterinterpretation is a variant of this method: a counterinterpretation is an argument in the same logical form as a given argument, but a model of the premise-set is not a model of the conclusion. In a counterargument one changes the language but leaves its interpretation fixed; in a counterinterpretation one leaves the language fixed but changes its meaning. The methods of counterargument and counterinterpretation are both established on the ontic principle that two arguments in the same form11 are either both valid or both invalid. This principle of form makes it possible to reduce the invalidity of arguments not obviously invalid to the invalidity of obviously invalid arguments. The following example, in which the invalidity of argument A1 is to be established and argument A2 is known to be a counterargument, illustrates the method of counterargument.

A1 A2

1. If two is prime then three is prime. (T) 1. If two is odd then three is odd.(T)

2. Three is prime. (T) 2. Three is odd.(T)

? Two is prime (T) ? Two is odd.(F)

4.2 Aristotle's method for establishing inconcludence and invalidity. At A4-6 Aristotle uses other methods to demonstrate which premise-pair patterns are inconcludent. Once grasping that Aristotle treats premise-pair patterns and that a sullogismos is a panvalid elemental argument pattern, we can see the metalogical character of his methods of invalidation. Accordingly, he demonstrates not the invalidity of arbitrary object language arguments but (1) the inconcludence of premise-pair patterns and, consequently, (2) the paninvalidity of the four argument patterns associated with each inconcludent pair in the standard syntax. In Aristotle's logic, panvalidity and paninvalidity are exhaustive for argument patterns; no pattern is neutrovalid. And in the case of premise-pair patterns, being concludent and inconcludent are likewise exhaustive.

Our first encounter in Prior Analytics with Aristotle's methods of invalidation is his treatment of the premise-pair pattern PaM, MeS (26a2-9), which follows his treatment of PaM, MaS | PaS (Barbara) and PeM, MaS | PeS (Celarent) in A4. He then immediately treats the premise-pair pattern PeM, MeS (26a9-13) in the same manner. These four considerations together exhaust all possible premise-pair patterns with sentences in the first figure. The passage at 26a2-9 provides Aristotle's fullest statement of his principal method of invalidation used in A4-6. Of the 34 premise-pair patterns that do not generate a sullogismos in the three figures, only in six instances is another method used and in two of these six instances he uses a third method.12 We here examine only his method of contrasted instances which covers 28 premise-pair patterns. Aristotle writes:

However, if the first extreme follows [i.e. belongs to] all the middle and the middle belongs to none of the last, there will not be a sullogismos of the extremes, for nothing necessarily results in virtue of these things being so. (26a2-5; emphasis added)

This sentence states a set of necessary relationships of three terms in two universal premises for not generating a sullogismos in the first figure. We take this passage to state a rule (a direct counterpart of those for the sullogismoi13) concerning the premise-pair pattern PaM, MeS, that no sentence is a logical consequence of two sentences fitting this pattern. Thus, Aristotle eliminates four argument patterns in the standard syntax from being sullogismoi. He continues:

For it is possible for the first extreme to belong to all as well as to none of the last. Consequently, neither a particular nor a universal conclusion results necessarily; and, since nothing is necessary because of these, there will not be a sullogismos. Terms for belonging to every are animal, man, horse; for belonging to none, animal, man, stone. (26a5-9; emphasis added)

Aristotle clearly uses neither the method of counterargument nor the method of counterinterpretation, each of which requires finding an instance of an argument having true premises and a false conclusion in the same form as a given argument. Rather, by substituting two sets of three terms for the schematic letters, he constructs two arguments each of whose premises are true sentences fitting the same premise-pair pattern and whose conclusions also are true sentences, but in the one argument it is an a sentence, in the other an e sentence. We can express what he says at 26a2-9 as follows.

Argument instance Schematic Truth Argument instance Schematic Truth pattern value pattern value

1. Animal belongs to every PaM T 1. Animal belongs to every PaM T man. man.

2. Man belongs to no horse. 2. Man belongs to no stone. MeS T MeS T

? Animal belongs to every PaS T ? Animal belongs to no stone. PeS T horse. ? Animal does not belong to ? Animal belongs to some some stone. horse. PiS T PoS T

For Aristotle this demonstrates that "nothing necessarily results" from sentences is this premise-pair pattern since, as he shows, the results "could be otherwise". Thus, any sentences of three terms fitting this premise-pair pattern are shown never to result together in a valid argument: no sullogismos of the extremes through a middle is possible. This premise-pair pattern is thereby shown to be inconcludent. Aristotle does not explicitly treat i and o sentences as possible results, although his implicitly doing so is suggested at 26a6-7 by his writing that "neither a particular nor a universal conclusion results necessarily". It is evident, moreover, that he treats at one in this way four argument patterns in the standard syntax for each premise-pair pattern; he does not show that each of the four patterns is paninvalid by using counterarguments in each case.

Aristotle's method of contrasted instances is easily adapted to the method of counterargument. Both methods achieve the same results. We can apply Aristotle's two sets of three terms to the two argument patterns but switch the terms for belonging to none to belonging to every and vice versa. Thus:

Argument instance Schematic Truth Argument instance Schematic Truth pattern value pattern value

1. Animal belongs to every man. PaM T 1. Animal belongs to every PaM T man. 2. Man belongs to no stone. 2. Man belongs to no horse. MeS T MeS T

? Animal belongs to every PaS F ? Animal belongs to no horse. PeS F stone. ? Animal does not belong to ? Animal belongs to some stone. some horse. PiS F PoS F

In these cases the premises are all true sentences and the respective conclusions are false sentences. Here, then, are counterarguments for the arguments provided by Aristotle, which may serve as modern counterparts to Aristotle's ancient method. It is apparent that Aristotle does not use this method in A4-6.

It is evident, then, that Aristotle's focus in Prior Analytics A4-7 is on the formal matters of logic, in particular, on determining which argument patterns have all valid instances and just as surely on determining which argument patterns have all invalid instances. He makes there determinations without special reference to semantic matters, or, that is, by assuming the semantic unambiguity of terms substituted for his schematic letters so as not to alter an argument's logical pattern. The result of his logical investigations, then, enables him to determine the validity or invalidity of a given 'syllogistic' argument by virtue of its form alone. He has identified all the argument patterns whose instances, in the case of valid arguments, have conclusions which follow logically from premises. Aristotle's accomplishment to establish the epistemic value of these formal results should not be underplayed.

5.0. Fallacious argumentation in Sophistical Refutations. In Sophistical Refutations Aristotle treats sophistic and eristic argumentation. He refers to this kind of reasoning as producing phainomenoi sullogismoi or apparent sullogismoi. These are arguments that appear to be sullogismoi and refutations (elenchoi) but which are really instances of faulty reasoning. Aristotle has a somewhat broad notion of a sophistical argument: "by a sophistical refutation and sullogismos I mean not only a sullogismos or refutation which appears to be valid but is not, but also one which, though it is valid, only appears to be appropriate to the thing in question" (SR8). Below we only treat those fallacies which appear to produce a refutation and not those arguments that are valid but which draw an , such as the of treating as cause what is not cause (SR5, 29).14

At the outset of Sophistical Refutations Aristotle identifies a pervasive source of error that serves as a theme throughout the treatise. He attributes most mistakes in reasoning to a person's inexperience with the formal matters of argumentation, with the semantic matters of language, and with having insufficient information. He writes:

Both sullogismos and elenchos are sometimes genuine and sometimes not, though inexperience may make them appear so-for inexperienced people obtain only, as it were, a distant view of these things. For a sullogismos rests on certain statements such that they involve necessarily the assertion of something other than what has been stated, through what has been stated; an elenchos is a sullogismos to the contradictory of the given conclusion. Now some of them do not really achieve this, though they seem to do so for a number of reasons; and of these the most prolific and usual is the argument that turns upon names. It is impossible in a discussion to bring in the actual things discussed: we use their names as symbols instead of them; and we suppose that what follows in the names, follows in the things as well-For names are finite and so is the sum-total of accounts, while things are infinite in number. Inevitably, then, the same account and a single name signify several things. In the same way in arguments too those who are not well acquainted with the force of names misreason both in their own discussions and when they listen to others. (SR1: 164b25-165a17; cf. SR33)15

Aristotle alerts his readers, both those who intend to engage publicly in disputation and those wishing privately to improve their own reasoning, to two matters. On the one hand, there are the formal matters of argumentation and, on the other hand, there is the matter of the content, the 'what' that is treated in an argumentation. Aristotle asks for precision in both matters. In this connection, we cite at length Aristotle's synopsis at SR7 on the causes of error in respect of each genus of fallacy, namely, the six that depend upon the language used and the seven independent of the language used. Both sources of error indicate his attention to semantic matters in relation to an underlying logical syntax.

The error comes about in the case of arguments that depend on and [ambiguity] because we are unable to distinguish the various (for some terms it is not easy to distinguish, e.g. one, being, and sameness), while in those that depend on combination and division, it is because we suppose that it makes no difference whether the phrase is combined or divided, as is indeed the case with most phrases. Likewise also with those that depend on accent-With those that depend on the form it is because of the likeness of expression. For it is hard to distinguish what kind of things are signified by the same and what by different kinds of expression (for a man who can do this is practically next door to the understanding of the truth, and knows best how to assent) because we suppose every predicate of anything to be an individual thing, and we understand it as being one thing; for it is to that which is one and to substances that individuality and being seem especially to belong.- With those fallacies that depend on , error comes about because we cannot distinguish what is the same and what is different, what is one and what many, or what kinds of predicate have all the same accidents as their subject. Likewise also with those that depend on the consequent; for the consequent is a branch of accident. Moreover, in many cases it seems and it is claimed that if this is inseparable from that, so also is that from this. With those that depend upon deficiency in the account of a refutation, and with those that depend upon the difference between a qualified and an unqualified statement, error consists in the smallness of the difference involved; for we treat the limitation to the particular thing or respect or manner or time as adding nothing to the meaning, and so grant a statement universally. Likewise also in the case of those that assume the original point, and those of false cause, and all that treat a number of questions as one; for in all of them the error lies in the smallness of the difference; for our failure to be quite precise in our definition of propositions and of sullogismoi is due to the aforesaid reason. (169a22-169b17; emphases added)

Lack of precision, relative to a particular person in respect of an inability to distinguish various senses of words and expressions or a failure to distinguish what is the same and what is different, points to a person's inexperience with linguistic usage and meaning and with scientific and philosophical understanding, and, we may add, with ignorance of what a sullogismos is. Aristotle in Sophistical Refutations also draws attention to a person's inexperience not only with public disputation, for example, by not having secured a statement that has a single meaning, but only one that appears to have (see, e.g. SR10 on not distinguishing the word from the or the thing signified), but also with other semantic and formal matters of argumentation, for example, not recognizing that the conclusion may follow not in fact but only verbally (SR8). In this latter respect also consider his reducing all thirteen fallacies to ignoratio elenchi or ignorance of what a sullogismos is. Moreover, a passage at SR6 reminds of us of what Aristotle writes in De Interpretatione and Prior Analytics on propositions. He writes:

Those fallacies that depend upon the making of several questions into one consist in our failure to articulate the account of a proposition. For a proposition predicates a single thing of a single thing. For the same definition applies to one single thing only and to the thing without qualification, e.g. to man and to one single man only; and likewise also in other cases. If, then, a single proposition is one which claims a single thing of a single thing, a proposition, without qualification, will be the putting of a question of that kind. Now since a sullogismos starts from propositions and a refutation is a sullogismos, a refutation, too, will start from propositions. (169a6-14)

Surely, knowledge of 'formal' logic is crucial for reasoning well, whether in constructing an argumentation or in defending oneself from refutation. In particular, attention must be directed to how terms of different semantic categories determine different underlying logical forms.

Below we show that Aristotle's use of 'sullogismos' in Sophistical Refutations denotes an argument that fits a panvalid argument pattern as treated in Prior Analytics and that 'phainomenos sullogismos' denotes an argument that appears to fit such a pattern. However, such an argument really fits another pattern, for example, one with four terms as in a case of equivocation, which is not a sullogismos at all. A sophistical refutation or phainomenos sullogismos, as we treat it below, is an argument that appears to be a sullogismos but is really an invalid argument. As Aristotle remarks, such arguments need solution, whether a refutation or a proof of their invalidity.

5.1 Equivocation and ambiguity. Aristotle recognizes three varieties of equivocation and ambiguity: "[1] when either the account or the name properly signifies more than one thing ... [2] when by custom we use them so,-[3] when words that have a simple taken alone have more than one meaning in combination" (SR4). At SR17 he addresses solving erroneous reasoning when fighting eristic persons by treating them not as refuting, but as merely appearing to refute. He writes at 175a36-175b3 (emphases added): For if refutation is a non-equivocal contradiction arrived at from certain premises, there will be no need to draw distinctions against ambiguity and equivocation; for they do not effect a sullogismos. The only motive for drawing further distinctions is that the conclusion reached looks like a refutation. What, then, we have to beware of, is not being refuted, but seeming to be, because of course the asking of ambiguities and of questions that turn upon equivocation, and all the other tricks of that kind, both conceal a genuine refutation and make it uncertain who is refuted and who is not.

His comments here are complemented by what he says at SR17 that if people never made two questions into one question, the fallacies relating to equivocation and ambiguity would never arise, rather there would either be genuine refutation or none at all. He continues:

Accordingly wherever it is uncertain in which of two senses the premiss proposed is usually meant- whether as maxims are (for people call both true opinions and general assertions maxims), or like 'the diagonal of a square is incommensurate with its side'; and moreover whenever opinions are divided as to the truth, we then have subjects of which it is very easy to change the terminology undetected. For because of the uncertainty in which of the two senses the premiss contains the truth, one will not be thought to be playing any trick, while because of the division of opinion, one will not be thought to be telling a falsehood; for the change will make the position irrefutable. (176b17-25)

Aristotle recognizes that a case of equivocation amounts to an argument appearing to be an instance of a given sullogismos, that is, of a given panvalid argument pattern. However, the argument is really an instance of another pattern, usually one having four terms and not three, and not valid. This condition is disguised by a linguistic phenomenon not immediately recognized by a participant who takes the argument to be a sullogismos. Thus, while the grammatical pattern makes the argument seem to conform to one of the sullogismoi, its underlying logical pattern is different.

We take the following example of equivocation from SR4 to illustrate Aristotle's thinking and to show that underlying his thinking are the formal considerations reached in Prior Analytics A4-7.

Or again, "Evils are good, for what must exist is good, and evil must exist". Here "must exist" is used in two senses; it means "what is necessary", which is often true of evils (for some evil is necessary), and we also say that good things "must [ought to] exist". (165b34-38)

This argument may be expressed more formally by using Aristotle's 'syllogistic' methods as follows (schematic letters as above, premises numbered, conclusion indicated by '?').

Argument: phainomenos-sullogismos Argmnt: Sentence Apprnt Apprt abbrev term patterns argmnt truth constants pattern value

1. Good [G] belongs to every that which must exist [M]. 1. GaM 1. PaS 1. PaM T

2. That which must exist belongs to some evil [E].

? Good belongs to some evil. 2. MiE 2. PiS 2. MiS T

? GiE ? PiS ? PiS F This argument appears to fit the pattern Barbara, and thus it appears also that the conclusion follows necessarily from the premises. The absurdity is that, while the premises are thought to be true, the conclusion is thought to be false but nevertheless to follow logically. Taking Aristotle's comments on the equivocal use of 'must exist', we can recast the argument to make explicit its underlying logical pattern as follows, and thus we can recognize it to be an instance of a phainomenos sullogismos or a non-sullogismos, that is, an invalid argument ('X' and 'Z' are also used as schematic letters).

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev patterns pattern value term constants

1. Good [G] belongs to every that which ought to exist 1. GaO 1. PaS 1. PaX T [O].

2. That which is necessary [N] belongs to some evil [E]. 2. NiE 2. PiS 2. ZiS F ? Good belongs to some evil.

? GiE ? PiS ? PiS F

Here we see that there is no middle but a fourth term. Aristotle provides three other instances of equivocation at SR4. Two of them follow.

'The same man is both seated and standing and he is both sick and in health; for it is he who stood up who is standing, and he who was recovering who is in health; but it is the seated man who stood up, and the sick man who was recovering.' For 'The sick man does so and so', or 'has so and so done to him' is not single in meaning: sometimes it means the man who is sick now, sometimes the man who was sick formerly. Of course, the man who was recovering was the sick man, who really was sick at the time; but the man who is in health is not sick at the same time: he is the sick man in the sense not that he is sick now, but that he was sick formerly.

Argument: phainomenos-sullogismos Argmnt: Sentence Apparnt Apprttruth abbrev patterns argmnt value term pattern constants

1. Standing [T] belongs to every person who stood up 1. TaW 1. PaS 1. PaM T [W].

2. Person who stood up belongs to every seated man [M]. 2. WaM 2. PaS 2. MaS T

? Standing belongs to every seated man. ? TaM ? PaS ? PaS F

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev patterns pattern value term constants

1. Standing [T] belongs to every person who stood up [W]. 1. TaW 1. PaS 1. PaM T

2. Person who stood up belongs to every seated man [M].

? Standing belongs to every formerly seated man [F]. 2. WaM 2. PaS 2. MaX T

? TaF ? PaS ? PaZ T

Argument: phainomenos-sullogismos Argmnt: Sentence Apprnt Apprt abbrev patterns argmnt truth term pattern value constants

1. Being in health [H] belongs to every was recovering [R]. 1. HaR 1. PaS 1. PaM T

2. Was recovering belongs to every sick man [K].

? Being in health belongs to every sick man. 2. RaK T 2. PaS 2. MaS ? HaK F ? PaS ? PaS

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev patterns pattern value term constants

1. Being in health belongs to every was recovering. 1. HaR 1. PaS 1. PaM T

2. Was recovering belongs to every sick man while ailing. 2. RaK 2. PaS 2. MaX T

? Being in health belongs to every formerly sick man [F]. ? HaF ? PaS ? PaZ T

In these two cases the third or minor term is used equivocally to make the subject term of the conclusion a fourth term. At SR22, in addressing fallacies of identical form of expression, Aristotle notes that the same thing happens in these cases as happens in cases of equivocation: "for in dealing with the tyro in argument supposes that the fact and not the name which he affirmed has been denied". Aristotle cites the following argument with its solution.

'Does a man tread upon what he walks through?-But he walks through a whole day'. But the words denote not what he walks through, but when he walks.

Argument: phainomenos-sullogismos Argmnt: Sentence Apprnt Apprt abbrev patterns argmnt truth term pattern value constants

1. A man's treading upon [T] belongs to every a man's 1. TaW 1. PaS 1. PaM T walking through [W].

2. A man's walking through belongs to every whole day [D]. 2. WaD 2. PaS 2. MaS T ? A man's treading upon belongs to every whole day.

? TaD ? PaS ? PaS F

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev term patterns pattern value constants

1. A man's treading upon [T] belongs to every a man's 1. TaW 1. PaS 1. PaX T spatially walking through [W].

2. A man's [temporally] walking through [R] belongs to every 2. RaD 2. PaS 2. ZaS T whole day [D].

? A man's treading upon belongs to every whole day. ? TaD ? PaS ? PaS F

Here the 'would-be' middle term is used equivocally. This argument could be remedied by addressing the equivocation in the following way, which eliminates both the appearance of a sullogismos and a case of an invalid argument by producing a sullogismos. Consider the following: Argument: a sullogismos but not a refutation Argmnt: Sentence Argmnt Truth abbrev patterns pattern value term constants

1. A man's [spatially] treading upon [T] belongs to no a 1. TeW 1. PeS 1. PeM T man's[temporally] walking through [W].

2. A man's[temporally] walking through belongs to 2. WaD 2. PaS 2. MaS T every whole day [D].

? A man's [spatially] treading upon belongs to no whole day. ? TeD ? PeS ? PeS T

We can now see that the above arguments really fit other logical patterns, in most cases one with four terms, and thus these arguments are not sullogismoi at all. In such cases Aristotle recognizes that a given word or expression may have two different meanings and thus fall into two different semantic domains/categories, or denote two different terms. Thus, while an argument with an equivocal expression has a given grammatical pattern that makes it appear to be a sullogismos, it really has an underlying logical pattern different than a sullogismos.

It is similar with ambiguity: while a given argument with an ambiguity has one grammatical pattern, which helps to make it appear to be a sullogismos, it really has two underlying logical patterns. At SR4 Aristotle cites five cases of ambiguity, two of which are arguments: First: 'There must be sight of what one sees; one sees the pillar; ergo the pillar has sight'.

Argument: phainomenos-sullogismos Argmnt: Sentence Apprnt Apprt abbrev term patterns argmnt truth constants pattern value

1. Sight [S] belongs to every what is seen [W]. 1. SaW 1. PaS 1. PaM T

2. What is seen belongs to some pillar [P]. 2. WiP 2. PiS 2. MiS T

? Sight belongs to some pillar. ? SiP ? PiS ? PiS F

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev term patterns pattern value constants

1. Being seen [B] belongs to every what is seen [W]. 1. BaW 1. PaS 1. XaM T

2. What is seen belongs to some pillar [P]. 2. WiP 2. PiS 2. MiS T ? Having capacity to see [S] belongs to some pillar ? SiP ? PiS ? ZiS F

This argument might also be addressed in the following way, in which case we produce a sullogismos.

Argument: an instance of a sullogismos Argmnt: Sentence Argmnt Truth abbrev term patterns pattern value constants

1. Being seen [B] belongs to every what is seen [W]. 1. BaW 1. PaS 1. PaM T

2. What is seen belongs to some pillar [P]. 2. WiP 2. PiS 2. MiS T ? Being seen [B] belongs to some pillar ? BiP ? PiS ? PiS T

The second argument-"What you profess to be, that you profess to be; you profess a stone to be; ergo you profess to be a stone."-is more difficult to formalize strictly and at the same time preserve the effect. Still, however, consider the following:

Argument: phainomenos-sullogismos Argmnt: Sentence Apprntargmnt Apprttruth abbrev patterns pattern value term constants

1. Your professing that to be [B] belongs to every 1. BaE 1. PaS 1. PaM T your professing something to be [E].

2. Your professing something to be belongs to some stone [S]. 2. EiS 2. PiS 2. MiS T

? Your professing that to be belongs to some stone. ? BiS ? PiS ? PiS F

Argument: non-sullogismos Argmnt: Sentence Agmnt Truthvalue abbrev patterns pattern term constants

1. Your professing that to be [B] belongs to every your 1. BaE 1. PaS 1. XaM T professing something to exist [E].

2. Your professing something to exist belongs to some 2. EiS 2. PiS 2. MiS T stone [S].

? Your professing to be that [T] belongs to some stone. ? TiS ? PiS ? ZiS F

The other meaning of this argument expresses a sullogismos as follows.

Argument: a sullogismos Argmnt: Sentence Agmnt Truthvalue abbrev patterns pattern term constants

1. Your professing that to exist [B] belongs to every your 1. BaE 1. PaS 1. PaM T professing something to exist [E].

2. Your professing something to exist belongs to some stone [S]. 2. EiS 2. PiS 2. MiS T

? Your professing that to exist [T] belongs to some stone. ? BiS ? PiS ? PiS T

5.2 Combination and division. Aristotle at SR4 treats the fact that the meanings of words in combination and in division differ; but there he does not provide examples of faulty arguments. At SR20 he takes up solving refutations that depend on division or combination. The following is one of his argument examples (177a36-177b12).

'Was he being beaten with that with which you saw him being beaten?' and 'Did you see him being beaten with that with which he was being beaten?' This has also in it an element of ambiguity in the questions, but it really depends upon combination. -It is evident also that not all refutations depend upon ambiguity as some people say they do. The answerer, then, must divide the expression; for to see a man being beaten with my eyes is not the same as to say I saw a man being beaten with my eyes.

Formalizing this argument 'syllogistically' we have the following:

Argument: phainomenos-sullogismos Argmnt: Sentence Apprnt Apprnt abbrev patterns argmnt truth term pattern value constants

1. Being beaten with that with which I saw him being beaten 1. BaS 1. PaS 1. PaM T [B] belongs to every that with which I saw him being beaten [S].

2. That with which I saw him being beaten belongs to every 2. SaE 2. PaS 2. MaS T my eyes [E].

? Being beaten with that with which I saw him being beaten belongs to every my eyes. ? BaE ? PaS ? PaS F

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev term patterns pattern value constants

1. Being beaten with that with which I saw him being beaten 1. BaS 1. PaS 1. XaM T [B] belongs to every that with which I saw him being beaten [S].

2. That with which I saw him being beaten belongs to every my eyes [E]. 2. SaE 2. PaS 2. MaS T

? Being beaten with the thing which I saw him being beaten [T] belongs to every my eyes. ? TaE ? PaS ? ZaS F

5.3 Without qualification or not without qualification. Aristotle treats the fallacy of using an expression without qualification or not without qualification but with some qualification of respect, or place, or time, or relation. Of the four examples there we cite the following.

'What is, is not, if it is not a particular kind of being, e.g. if it is not a man.' For it is not the same thing not to be something and not to be without qualification: it looks as if it were, because of the closeness of the expression, i.e. because to be something is but little different from to be, and not to be something from not to be.

Argument: phainomenos-sullogismos Argmnt: Sentence Apprnt Appnt abbrev term patterns argmnt truth constants pattern value

1. Not to be something [N] belongs to every man [M]. 1. NaM 1. PaS 1. PaM T

2. Man belongs to some what is[W]. 2. MiW 2. PiS 2. MiS T ? Not to be something belongs to some what is. ? NiW ? PiS ? PiS F

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev patterns pattern value term constants

1. Not to be something (unqualified) [N]belongs to every man 1. NaM 1. PaS 1. XaM F [M].

2. Man belongs to some what is [W]. 2. MiW 2. PiS 2. MiS T

? Not to be something else in particular (qualified) [E] belongs to some what is. ? EiW ? PiS ? ZiS T

Now the absurdity is resolved because the underlying logical pattern has been made evident. At SR25 Aristotle provides other examples relating to solving those fallacies without qualification or not without qualification. Consider the following two.

'Is health, or wealth, a good thing?-But to the fool who does not use it a LEFT it is not a good thing; therefore it is both good and not good'.

Argument: phainomenos-sullogismos Argmnt: Sentence Apprntargmnt Apprt abbrev term patterns pattern truth constants value

1. Good [G]] belongs to every wealth [W]. 1. GaW 1. PaS 1. PaM T

2. Wealth belongs to some bad thing [B]. 2. WiB 2. PiS 2. MiS T

? Good belongs to some bad thing. ? GiB ? PiS ? PiS F

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev patterns pattern value term constants

1. Good [G]] belongs to every wealth (unqualified) 1. GaW 1. PaS 1. PaX T [W].

2. Wealth (qualified) [F] belongs to some bad thing [B]. 2. FiB 2. PiS 2. ZiS T ? Good belongs to some bad thing. ? GiB ? PiS ? PiS F

'Is that which the prudent man would not wish, an evil?-But he would not wish to lose the good; therefore the good is an evil'. But it is not the same thing to say that the good is an evil and to lose the good is an evil. Similarly with the argument of the thief: for it is not the case that if the thief is an evil thing, acquiring things is also evil; what he wishes, therefore, is not what is evil but what is good; for to acquire is good.

Argument: phainomenos-sullogismos Argmnt: Sentence Apprnt Apprttruth abbrev patterns argmnt value term pattern constants

1. Evil [E] belongs to every what the thief wishes [T]. 1. EaT 1. PaS 1. PaM T

2. What the thief wishes belongs to every acquiring things [A]. 2. TaA 2. PaS 2. MaS T ? Evil belongs to every acquiring things.

? EaA ? PaS ? PaS F

Argument: non-sullogismos Argmnt: Sentence Argmnt Truth abbrev patterns pattern value term constants

1. Evil [E] belongs to every what the thief wishes 1. EaT 1. PaS 1. PaX T (unqualified, viz. stealing) [T].

2. What the thief wishes (qualified) [Q] belongs to every 2. QaA 2. PaS 2. ZaS F acquiring things [A].

? Evil belongs to every acquiring things. ? EaA ? PaS ? PaS F

Aristotle remarks in general on the causes of this fallacy at SR5. An occurrence of this fallacy depends upon whether an expression is used without qualification or in a certain respect and not strictly, that is, when an expression is used in a particular sense but is taken without qualification.

5.3 Consequent. At SR5 Aristotle explicitly attributes the causes of the refutation which depends upon the consequent to a person's supposing that the relation of consequence is convertible: "For whatever, if this is the case, that necessarily is the case, they then suppose also that if the latter is the case, the former necessarily is the case". Mentioning that this also happens in syllogistic reasoning, he cites Melissus' argument at SR5 (interestingly, Aristotle remarks on this argument at three places: SR5, 6, and 28).

Melissus' argument that the universe is infinite, assumes that the universe has not come to be (for from what is not nothing could possibly come to be) and that what has come to be has done so from a first beginning. If, therefore, the universe has not come to be, it has no first beginning, and is therefore infinite. But this does not necessarily follow; for if what has come to be always has a first beginning, it does not follow that what has a first beginning has come to be; any more than it follows that if a man in a fever is hot, a man who is hot must be in a fever. (167b13- 20)

We may rewrite this argumentation formally as a deduction as follows.

Argument: phainomenos-sullogismos Argmnt: Explanation Truth abbrev value term constants

1.No beginning [N] belongs to every ungenerated 1. NaU. 1. Premise T [U].

2.Infinite [I] belongs to every ungenerated. 2. IaU. 2. Premise T

3.No beginning belongs to every universe [W]. 3. NaW. 3. Premise T

? Infinite belongs to every universe. ? IaW. ? Conclusion

4.Ungenerated belongs to every no beginning. 4. UaN. 4. 1 a-conversion T

5.No beginning belongs to every universe. 5. NaW. 5. 3 repetition T

6.Ungenerated belongs to every universe 6. UaW. 6. 4,5 Barbara T

7.Infinite belongs to every ungenerated. 7. IaU. 7. 2 repetition T

8.Ungenerated belongs to every universe. 8. UaW. 8. 6 repetition T

9.Infinite belongs to every universe. 9. IaW. 9. 7,8 Barbara T

Here we can see that the fault of this apparent deduction is to convert at step 4an a-sentence, which does not admit of simple (but of per accidens) conversion. We can compare the mistake here and Aristotle's example of the 'man with a fever' to his instruction at Prior Analytics A2 where he treats conversion.

6. Concluding remarks. We have reviewed Aristotle's metalogical accomplishments at Prior Analytics A4-7 and seen that he consciously worked with 'syllogistic' argument patterns and that he recognized these patterns to be abstract or formal objects, that is, to be relatively uninterpreted objects. In this respect, then, we can appreciate Aristotle to distinguish a given argument's underlying logical syntax both from its subject matter and its semantics. While it is doubtful that Aristotle held a modern theory of language, it is nevertheless evident that he recognized different argument patterns to underlie sentences in arguments involving, for example, ambiguity and equivocation. In just this connection, we can appreciate his logical acumen in recognizing that linguistic expressions (words and phrases) have different meanings; accordingly, the same expression might fall into different semantic domains and thus represent different terms. As we have seen, using Aristotle's 'artificial' categorical syllogistic syntax, ambiguous or equivocal terms disguise different logical . Repeatedly Aristotle alerts his readers to the necessity for drawing distinctions. It is this recognition, we believe, that prompted his referring to the faulty reasonings treated in Sophistical Refutations as phainomenoi sullogismoi, that is, as arguments that appear to fit given sullogismoi- given panvalid elemental argument patterns-but which in truth have different underlying logical syntaxes. Indeed, the lessons in Sophistical Refutations that we have reviewed are the more intelligible if one understands Aristotle to have worked with a clear notion of an argument's pattern into which fit, for example, ambiguous expressions that give the appearance of correct reasoning. He may even, we suggest, have presupposed in Sophistical Refutations the metalogical findings of his logical investigations in Prior Analytics, notwithstanding the generally accepted order of his having written these treatises. We may recall what Aristotle says at SR11, that "he is a dialectician who examines by the help of a theory of sullogismos [deduction]", to indicate his attention to the formal matters of reasoning, which are properly treated as subject matter for the of logic.

Notes

1. Aristotle defines sullogismos at: Prior Analytics 24b18-20, Topics 100a25-27, Sophistical Refutations 164b27-165a2, and Rhetoric 1356b16-18. This statement is from Prior Analytics. We transliterate 'sullogismos' rather than translate by "deduction" or even "syllogism" to help objectify its meaning; cf. J. Gasser 1991.

2. J. N. Keynes, for example, typical of the traditionalist interpretation, cites six of the syllogism (1906: 287-291; cf. R. M. Eaton 1959: 95-100). It is interesting to note that, while traditionalists are concerned with correct reasoning in their treatment of syllogisms, they do not understand Aristotle to work with a natural deduction system and they entirely miss Aristotle's concern with the epistemic process of deduction.

3. Corcoran's terminology, with its refined determinations, is especially useful for making sense of Aristotle's logical investigations. Moreover, beyond their applicability to studies of Aristotle's logic, they are an important contribution toward improving the intelligibility of discourse on logic and refining matters of logic.

4. This is evident from the of his logical investigations themselves and from how Aristotle understands the relationship of the two Analytics. Cf. Aristotle's discussion on the relatively topic neutral character of the common notions related to treating quantities at Metaphysics 1061b20-21. Consider also in Prior Analytics A1 where he remarks that demonstrative and dialectical argumentation equally syllogize (sullogizesthai) and in Sophistical Refutations that didactic, dialectical, examination, and contentious arguments also equally syllogize. Especially see Sophistical Refutations 9 where he states that the dialectician is not concerned with a particular subject matter of argumentation but with what is common to every art and faculty (170a35-36).

5. With deductionists, then, we take Aristotle to have genuine proof-theoretic interests. On Aristotle's having proof- theoretic interests, see R. Smith 1984: 594-596, 1986: 55-61, and 1991: 48-50. J. Corcoran (1974, 1994) and R. Smith (1989) have generally made Aristotle's case in this respect.

6. J. Corcoran (1974: 100) has called these "metalinguistic variables"; cf. R. Smith (1984: 590, 595) who refers to them as "syntactic variables for terms". We believe that Aristotle takes his letters to be schematic letters in a way similar to W. Quine's meaning (1970:12; 1982: 33, 145-146, 160-162, 289, 300-301).

7. Note that Aristotle specifically converts the derived sentence patterns in Camestres and Disamis to preserve this syntax.

8. We use, with some modifications, R. Smith's translation of Prior Analytics (1989) to cite Aristotle's text in translation.

9. The traditional names of the sullogismoi are: First figure-Barbara, Celarent, Darii, Ferio; second figure-Cesare, Camestres, Festino, Baroco; third figure-Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison.

10. Modern logicians refer to the validity of an argument. Thus, a given sentence follows logically from other given sentences if it is implied by the other sentences, or if it is a logical consequence of the other sentences, or if all the information in the given sentence is contained in the other sentences, or if there exists no counterargument. An argument is invalid if one or none of the validity conditions holds.

11. While the distinction between "pattern" and "form" may not make a difference to Aristotle studies, it is very important for clearing up some confusion about establishing invalidity. We follow (1993: xxxi-xxxvii) in distinguishing form from pattern as follows. While a given sentence has only one logical form, it may fit a number of patterns. An argument, likewise, has only one form but may fit a number of patterns. The difference "pattern" and "form" is important especially for determining a given argument to be invalid by the method of counterargument. Every argument, for example, whatever its number of premises, fits the argument pattern 'premise-set-conclusion' (schematically 'P-c'), but obviously not every argument has the same logical form. While two arguments in the same logical form are either both valid or both invalid, some arguments in a given pattern may be valid while others are invalid. See also above section 3.1.

12. The method of contrasted instances works for almost all premise-pair patterns, noticeably failing in some instances when the minor premise is a particular, and usually a privative, sentence.

13. Take, for example, the sentence expressing the Barbara and Celarent rules at A4, 25b32-35 (cf. 25b37-39 [Darii], 25b40-26a2 [Ferio]). 'Barbara' is used both to denote the rule and to name the argument pattern.

14. We also do not consider fallacies based upon accent (SR4, 21), accident (SR5, 24), ignoratio elenchi (SR5, 6, 26), assuming the point (SR5, 27) and making several questions into one (SR5, 30) for similar reasons.

15. We use, with some modifications, W. A. Pickard-Cambridge's translation of Sophistical Refutations (1928) to cite Aristotle's text.

References Barnes, J. 1981. "Proof and the syllogism". In: E. Berti (ed.). Aristotle on Science: the "Posterior Analytics". Padua: Antenore, pp. 17-59.

Bolton, R. & R. Smith (eds.). 1994. Logic, Dialectic, and Science in Aristotle. Ancient Philosophy 14 (special issue).

Bochenski, I. M. 1957. Ancient Formal Logic. Amsterdam: North-Holland Publishing Co.

Bochenski, I. M. 1961. A History of Formal Logic. Notre Dame: University of Notre Dame Press.

Church, A. 1956. Introduction to Mathematical Logic, vol 1. Princeton: Princeton University Press.

Corcoran, J. 1974. "Aristotle's natural deduction system". In: J. Corcoran (ed.). Ancient Logic and Its Modern Interpretations. Dordrecht: D. Reidel Publishing Company, pp. 85-132.

Corcoran, J. 1983. "Deduction and reduction: two proof-theoretic processes in Prior Analytics I". Journal of Symbolic Logic 48, p. 906.

Corcoran, J. 1989. "Argumentations and logic". Argumentation 3, pp. 17-43.

Corcoran, J. 1993. "Editor's introduction". In: M. R. Cohen & E. Nagel. An Introduction to Logic. Indianapolis: Hackett Publishing Co., pp xvii-xlvi.

Corcoran, J. 1994. "The founding of logic". In: Bolton, R. & R. Smith. 1994, pp. 9-24.

Dorion, Louis-André (tr). 1995. Aristote: Les réfutations sophistique. Presses de l'Université Laval.

Eaton, R. M. 1959. General Logic. New York: Charles Scribner's Sons.

Forster, E. S. 1965. Aristotle: On Sophistical Refutations. Cambridge: Harvard University Press.

Frede, M. 1974. "Stoic vs. Aristotelian syllogistic". In: M. Frede. 1987. Essays in Ancient Philosophy. Minneapolis: University of Minnesota Press, pp. 99-124.

Gasser, J. 1991. "Aristotle's logic for the modern reader". History and Philosophy of Logic 12, pp. 235-240.

Hope, R. 1960. Aristotle: Metaphysics. Ann Arbor: University of Michigan Press.

Joseph, H. W. B. 1906. An Introduction to Logic. Oxford: Clarendon Press.

Keynes, J. N. 1906. Studies and Exercises in Formal Logic. London: Macmillan and Co., Ltd.

Kneale, W. & M. Kneale. 1962. The Development of Logic. Oxford: Clarendon Press.

Lear, J. 1980. Aristotle and Logical Theory. Cambridge: Cambridge University Press.

Lejewski, C. 1967. "Ancient logic". In: P. Edwards (ed.). The Encyclopedia of Philosophy. New York: Macmillan Publishing Co., Inc., vol. 4, pp. 513-520.

Lukasiewicz, J. 1958. Aristotle's Syllogistic from the Standpoint of Modern Formal Logic. Oxford: Oxford University Press. Miller, J. W. 1938. The Structure of Aristotelian Logic. London: Kegan Paul, Trench, Trubner & Co., Ltd.

Parry, W. T. & E. A. Hacker. 1991. Aristotelian Logic. Albany: State University of New York Press.

Patzig, G. 1968. Aristotle's Theory of the Syllogism: A Logico-Philological Study of Book A of the Prior Analytics. Dordrecht: D. Reidel Publishing Company.

Prior, A. N. 1955. Formal Logic. Oxford: Clarendon Press.

Pickard-Cambridge, W. A. (tr). 1928. Sophistical Refutations. In J. Barnes (ed). 1984. The Collected Works of Aristotle, vol 1. Princeton: Princeton University Press, pp 278-314.

Quine, W. v. O. 1970. Philosophy of Logic. Englewood Cliffs: Prentice Hall, Inc.

Quine, W. v. O. 1982. Methods of Logic. Cambridge: Harvard University Press.

Rose, L. 1968. Aristotle's Syllogistic. Springfield: Charles C. Thomas.

Ross, W. D. 1949. Aristotle's Prior and Posterior Analytics. Oxford: Clarendon Press.

Ross, W. D. 1953. Aristotle's Metaphysics. Oxford: Clarendon Press.

Ross, W. D. 1989. Aristotelis Analytica Priora et Posteriora. Oxford: Clarendon Press.

Ross, W. D. 1989. Aristotelis Topica et Sophistici Elenchi. Oxford: Clarendon Press.

Smiley, T. 1973. "What is a syllogism?". Journal of Philosophical Logic 2:1, pp. 136-154.

Smith, R. 1984. "Aristotle as proof theorist". Philosophia Naturalis 21: 2-4, pp. 590-597.

Smith, R. 1989. Aristotle: Prior Analytics. Indianapolis: Hackett Publishing Co.

Smith, R. 1994. "Dialectic and the syllogism". In: Bolton, R. & R. Smith. 1994, 133-151.

Tarski, A. 1936. "On the of logical consequence". In A. Tarski. 1990. Logic, Semantics, Metamathematics. Indianapolis: Hackett Publishing Co., Inc., pp 409-420.

View Commentary by D. Hitchcock

View Index of Papers and Commentaries

Return to Main Menu